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Magic Square Sets

Problem Description

We propose a collection of magic square problems for System Competition under ASP-RFC. These problems can be easily encoded using aggregates, in a nontrivial way (meaning they are not easily reduced to ASP-core), and thus may serve as benchmarks for testing the effectiveness of the aggregate handling by a solver. The problem instances can also be generated by adding additional constraints.

Input Predicates: data/1, num/1

Output Predicates: sqr/3

Normal magic squares: a magic square of order 'n' is an arrangement of n2 numbers -- 1..n2 -- in a square, such that the 'n' numbers in all rows, all columns, and both diagonals sum to the same constant n*(n^2+1)/2. It is known that the magic square of any order exists. But the exact complexity is unknown to our best knowledge.

Semimagic squares: it is a relaxed normal magic square in the sense that only the rows and columns but not necessarily the diagonals sum to the magic constant n*(n2+1)/2.

Panmagic squares: a panmagic square is a magic square with the additional property that the broken diagonals, i.e. the diagonals that wrap round at the edges of the square, also add up to the magic constant n*(n2+1)/2. The Number of distinct (modulo rotation and reflection) panmagic square of order n=1,2,3,4,5,6 are 1, 0, 0, 48, 3600, 0 respectively. (Cf. http://oeis.org/searchq=panmagic+square&sort=&language=english&go=Search)

Associative magic squares: An associative magic square is a magic square for which every pair of numbers symmetrically opposite to the center sum up to the same value n^2+1. The number of distinct (modulo rotation and reflection) associative magic squares of order n=1,2,3,4,5,6 are 1,0,1,48,48544,0 respectively. (cf. http://oeis.org/search?q=associative+magic+square&sort=&language=english&go=Search)

Bimagic squares: A bimagic square is a magic square that also remains magic if all of the numbers it contains are squared.

Trimagic squares: A trimagic square is a magic square that also remains magic if all of the numbers it contains are squared or cubed. In the benchmark, we require for the cubed cases only.

Input format

Output format

Example

Author(s)

ASP Competition 2011: ProblemsDescription/MagicSquareSets (last edited 2011-01-10 10:20:58 by CarmenSantoro)